The acceleration mechanism for protostellar outflows is still uncertain, de
spite many dynamical studies. Active acceleration processes are expected to
heat the molecular gas, and it should be possible to choose between the po
ssible outflow models by excitation studies which measure the temperatures
of the molecular gas. We show how temperature predictions can be made from
a simple bow-shock driven shell model and compared with temperature estimat
es from excitation studies. As the momentum-conserving shell expands the ki
netic energy lost is sufficient to heat the molecular gas to temperatures m
any times that of the ambient cloud. The energy transfer - and therefore th
e temperature - is greatest near to the bow shock and therefore the tempera
ture rises with distance from the star. We present a multitransition CO stu
dy of the young outflow L383 and compare temperature predictions from the s
hell model with measurements of the CO excitation.